First slide

Doppler

Question

A jet plane passes over an aerodrome with a velocity 200 m/s at a height of 490 metre (see fig.). It

constantly blows a whistle of 1 kHz. If it passes over the ground crew, in one second then the change in frequency observed by the staff in this interval will be (if velocity of sound v= 340 m/s)

Moderate

A

620 . 3 Hz
B

238 .6 Hz
C

720.8Hz
D

820. 2Hz

Solution

From figure (13),
$\cos θ = \frac{100}{500} = \frac{1}{5} The frequency heard by staff in initial position n^{'} = n (\frac{v}{v - v_{s} \cos θ}) = 1000 \times \frac{340}{340 - 200 \times (1 / 5)} = 1133 \cdot 33 Frequency heard by staff in final position n^{n} = n (\frac{v}{v + v_{s} \cos θ}) = 1000 \times (\frac{340}{340 + 200 \times (1 / 5)}) = 894 \cdot 73 Δn = n^{'} - n^{''} = 1133 \cdot 33 - 894 \cdot 73 = 238 \cdot 6 Hz$

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